NEW OSCILLATION CRITERIA FOR FIRST ORDER LINEAR DIFFERENTIAL EQUATIONS WITH NON-MONOTONE DELAYS

Emad R. Attia; Hassan A. El-Morshedy

doi:10.11948/20210402

2022 Volume 12 Issue 4

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Emad R. Attia, Hassan A. El-Morshedy. NEW OSCILLATION CRITERIA FOR FIRST ORDER LINEAR DIFFERENTIAL EQUATIONS WITH NON-MONOTONE DELAYS[J]. Journal of Applied Analysis & Computation, 2022, 12(4): 1579-1594. doi: 10.11948/20210402

Citation:

Emad R. Attia, Hassan A. El-Morshedy. NEW OSCILLATION CRITERIA FOR FIRST ORDER LINEAR DIFFERENTIAL EQUATIONS WITH NON-MONOTONE DELAYS[J]. Journal of Applied Analysis & Computation, 2022, 12(4): 1579-1594. doi: 10.11948/20210402

NEW OSCILLATION CRITERIA FOR FIRST ORDER LINEAR DIFFERENTIAL EQUATIONS WITH NON-MONOTONE DELAYS

Emad R. Attia^1,2,
Hassan A. El-Morshedy^2, ,

1.
Department of Mathematics, College of Sciences and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt

Corresponding author: Email: elmorshedy@yahoo.com(H. El-Morshedy)

Abstract

Abstract

This paper is concerned with the oscillation of the first order linear delay differential equation $ x'(t)+q(t) x(\tau(t))=0 $, $ t\geq t_0 $, where $ q, \tau \in C([t_0,\infty),[0,\infty)) $, $ \tau(t)\leq t $, such that $ \underset{t \rightarrow \infty} {\lim} \tau(t)=\infty $. Several new oscillation criteria of iterative and non-iterative types are obtained. Two examples are presented to show the strength and applicability of these criteria over known ones.
- Oscillation criteria /
- delay differential equations /
- non-monotone delay
MSC: 34C10, 34K11, 34K05

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References

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